Short answers, pulled from the story.
Bahadur Shah I was born on the 14th of October 1643 in Burhanpur as the second son of the Mughal emperor Aurangzeb and his Pothwari wife Nawab Bai. He was originally named Muhammad Mu'azzam before ascending the throne.
Bahadur Shah I ascended the Mughal throne on the 19th of June 1707 at the age of 64 after defeating his younger half-brother Muhammad Azam Shah at the Battle of Jajau. He subsequently defeated and killed his other rival brother Muhammad Kam Bakhsh in January 1708 to secure his rule.
Guru Gobind Singh met Bahadur Shah I in Agra in July 1707 and accompanied him on campaigns until the Guru died in October 1708. After the Guru's death, his successor Banda Bahadur led a revolt that forced Bahadur Shah I to leave the Deccan and fight a series of battles in Punjab to suppress the uprising.
Bahadur Shah I converted to Shia Islam and altered the public prayer to give the title wasi to Ali, the fourth caliph, in an attempt to consolidate power. This decision alienated the powerful Sunni clergy and the populace of Lahore, creating a political schism that destabilized the empire's religious unity.
Bahadur Shah I died during the night of the 27th to the 28th of February 1712 due to enlargement of the spleen. He was buried on the 15th of May in the courtyard of the Moti Masjid in Mehrauli and was succeeded by his son Jahandar Shah who ruled until 1713.